Zobrazeno 1 - 10
of 127
pro vyhledávání: '"Mantzavinos, Dionyssios"'
We establish the local Hadamard well-posedness of a certain third-order nonlinear Schr\"odinger equation with a multi-term linear part and a general power nonlinearity known as the higher-order nonlinear Schr\"odinger equation, formulated on a finite
Externí odkaz:
http://arxiv.org/abs/2406.15579
The Hadamard well-posedness of the nonlinear Schr\"odinger equation with power nonlinearity formulated on the spatial quarter-plane is established in a low-regularity setting with Sobolev initial data and Dirichlet boundary data in appropriate Bourga
Externí odkaz:
http://arxiv.org/abs/2403.15350
Autor:
Hennig, Dirk, Karachalios, Nikos I., Mantzavinos, Dionyssios, Cuevas-Maraver, Jesus, Stratis, Ioannis G.
The question of whether features and behaviors that are characteristic to completely integrable systems persist in the transition to non-integrable settings is a central one in the field of nonlinear dispersive equations. In this work, we investigate
Externí odkaz:
http://arxiv.org/abs/2307.16408
The large time $t$ asymptotics for scalar, constant coefficient,linear, third order, dispersive equations are obtained for asymptotically time-periodic Dirichlet boundary data and zero initial data on the half-line modeling a wavemaker acting upon an
Externí odkaz:
http://arxiv.org/abs/2307.14670
We establish local well-posedness for the higher-order nonlinear Schr\"odinger equation, formulated on the half-line. We consider the scenario of associated coefficients such that only one boundary condition is required, which is assumed to be Dirich
Externí odkaz:
http://arxiv.org/abs/2305.18202
Considered here is a class of Boussinesq systems of Nwogu type. Such systems describe propagation of nonlinear and dispersive water waves of significant interest such as solitary and tsunami waves. The initial-boundary value problem on a finite inter
Externí odkaz:
http://arxiv.org/abs/2210.03279
This work studies the initial-boundary value problem of the two-dimensional nonlinear Schr\"odinger equation on the half-plane with initial data in Sobolev spaces and Neumann or Robin boundary data in appropriate Bourgain spaces. It establishes well-
Externí odkaz:
http://arxiv.org/abs/2204.13005
Publikováno v:
In Wave Motion January 2025 132
Autor:
Hennig, Dirk, Karachalios, Nikos I., Mantzavinos, Dionyssios, Cuevas-Maraver, Jesús, Stratis, Ioannis G.
Publikováno v:
In Journal of Differential Equations 15 July 2024 397:106-165
A polynomial-in-time growth bound is established for global Sobolev $H^s(\mathbb T)$ solutions to the derivative nonlinear Schr\"odinger equation on the circle with $s>1$. These bounds are derived as a consequence of a nonlinear smoothing effect for
Externí odkaz:
http://arxiv.org/abs/2012.09933